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The use of the concepts and methods of functional analysis not only makes the theory of quantum entropy more uniform and lu cid, but it essentially simplifies and extends it. Topics covered include the theory of majorization, variational principles for Modular Theory and Auxiliaries. The heritage of quantum entropies from quantum mechanics is their strong relation to Hilbert space. Sufficient Channels and Measurements. Entropies for General Quantum Systems. The math ematical formalism is based on operator theory and mostly the language of operator algebras is used.

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The use of the concepts and methods of functional analysis not only makes the theory of quantum entropy more uniform and lu cid, but it essentially simplifies and extends it. Ohya , Denes Petz. The heritage of quantum entropies from quantum mechanics is their strong relation to Hilbert space. Modular Theory and Auxiliaries. It has emerged from the investigation of the natural differential geometric structure From Relative Entropy to Entropy. Channeling Transformation and Coarse Graining.

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